Let me preface this up front, I support the owner's right to exclude certain people from participating in racing. After all, anyone who has private property has the right to deny access to their property (we are talking about American constitutional law).
Sure, some people will claim anyone the state licenses to participate in racing should be able to participate at any racetrack in the state. This is not the case. The state licensing a person to participate in racing means as far as the state is concerned, the individual may participate in racing. Were the track be operated by the state or receive state funding, then you could make a case the rule of exclusion would be restricted but failing this, the track operator of a private track still retains the right to deny someone access.
Look at this way, if your town issued a permit to a salesperson to canvas door to door, does that mean you have to let this person into your house? Of course not, you have the right to close the door on the salesperson, permit or not. Both the horseman and the merchant make a living doing what they do but you, the owner of the private property, is the final arbiter as to who gets in and who doesn't.
This all said, doesn't mean the rule of exclusion can't be abused and when it does, even the most well-intentioned policy can become a mockery and when it does, it hurts the credibility of the stated reason for the policy. When you are a homeowner, you may not care, but if you run a commercial enterprise, you better be concerned for your success depends on the views of your customers.
One way the stated goal of exclusion can be torpedoed is when the operator races in overnight events at a track they operate. Let's say you have a personal trainer who gets a positive. The whole racing world will be watching what you do. You decide to let your trainer continue to race at your track for all the right reasons; reasons you can substantiate. There is a reason why trainer A gets to race and trainer B gets the boot. The problem is with the rules of exclusion, you will never say why trainers are banned versus why others continue to race. Hence, the rising voice of the horsemen can be heard claiming 'playing favorites', 'not applying the rules fairly', etc., loud enough so the customers with cash start wondering what is going on. After a while, your customer is going to wonder if you let 'this cheat' (their words) continue to race, how up and up is your racing?
Of course, if the operator doesn't race at the track he controls, no one will be able to claim favoritism and the integrity of the exclusionary policy remains intact. This is why track operators do a disservice to their own facilities where they race. Best to race at tracks you don't own so no one can claim favoritism.